NO.PZ2023091901000026
问题如下:
The market portfolio (M) contains the optimal allocation of only risky asset and no risky assets. Let the S1 be the Sharpe ratio of this market portfolio. There exists a risk-free asset. Initially, an investor is fully (100%) invested in M with a portfolio Sharpe ratio of S1. Subsequently, the investor borrows 30% at the risk-free rate, such that she is 130% invested in the market portfolio (M) where this leverage portfolio has a Sharpe ratio of S2。After the leverage (i.e., borrowing at the risk-free rate to invest +30% in M, is the investor still on the efficient frontier and how do the Sharpe ratios?
选项:
A.No (no longer efficient), and S2
No, but S2 = S1.
Yes (still efficient), but S2
Yes and S2 = S1.
解释:
The ability to borrowing or lend morphs the concave/convex efficient frontier into the linear CML; i.e., the leveraged portfolio is efficient with higher risk and higher return.
All portfolios on the CML have the same Sharpe ratio: the slope of the CML.
借用或借出的能力将凹/凸有效边界变为线性CML;
也就是说,杠杆投资组合具有较高的风险和较高的收益。
CML上的所有投资组合都有相同的夏普比率:CML的斜率。
有效前沿线不是那条曲线吗?借钱的组合不是在CML上,那个线没在EL上了啊?